HELSINKI, Sept 18 (Reuters) - The Finnish government has given conditional backing to an updated application from Finnish-Russian group Fennovoima to build a nuclear reactor in the north of the country, prompting the Greens to quit and weaken the ruling coalition.

The permit for the 1,200 megawatt plant, owned by Russian state-controlled Rosatom and some 40 Finnish companies, still has to pass a parliament vote, but that is seen as likely since most parliamentarians in the four biggest parties are expected to support the project.

The government's ministers voted 10 to seven in favour of the project and the Green party said it would as a result resign from the ruling coalition, which has seven months left in the office before a general election in April.

The departure of the Green Party's 10 MPs will leave the coalition with four parties and a slim parliament majority, having 102 MPs (including the speaker who is not allowed to vote) against the opposition's 98.

"It is clear that the situation becomes more challenging in terms of decision-making ... This is a rare situation in Finnish politics, but I wouldn't over-dramatize it. We just have to be careful and work as a team," centre-right Prime Minister Alexander Stubb told a news conference.

The Green Party exit comes as Finland's triple A-rated economy struggles to return to growth, reflecting sluggish growth at best in the euro zone as a whole, issues affecting domestic industry such as the decline of the paper sector, and the Ukraine crisis, which has cut exports.

FINNISH OWNERSHIP

Fennovoima's project could still fall as the government said it must boost its Finnish ownership by next summer to at least 60 percent. Currently, Finnish owners have committed to a stake of 52 percent, while Rosatom, which is also due to supply the reactor, has a stake of 34 percent.

Several investors have pulled out of the project costing between 4 billion euros ($5.2 billion) and 6 billion, while the Ukraine crisis has further complicated the search for funding.

Russia's prominent role in the project has raised concerns in Finland and Green party leader Ville Niinisto even accused the government of "Finlandisation", referring to the influence of the Soviet Union on Finland's politics during the Cold War.

Stubb said: "The ownership has raised a lot of debate. I understand the concern but I can assure that the plant will operate strictly under Finnish law."

Fennovoima won a general go-ahead for the plant in 2010 but changes in the planned reactor's size and supplier required a renewed approval. The plant is scheduled to start operating in 2024.

The government was also due to decide whether to extend a new nuclear permit for Teollisuuden Voima's (TVO) troubled Olkiluoto site, but that decision was set aside for later consideration. TVO's biggest owners include utility Fortum as well as paper firms UPM-Kymmene and Stora Enso. (1 US dollar = 0.7763 euro) (Reporting by Jussi Rosendahl; Editing by David Holmes)